Image Enhancement Methods With Sparsity Inducing Regularization Based On Generalized Gaussian Distribution

Image enhancement represents a set of image processing problems,which aims to adapt the images to specific applications.In this thesis,four problems of image enhancement will be discussed,including cross-modality face synthesis,image texture smoothing,image denoising,and image deblurring.With the booming of smart phones and digital cameras,these four image enhancement problems witness some practical applications.Meanwhile,the research on the four problems also provides us a platform to evaluate regularization models,from the perspective of theory.Maximum a posterior(MAP)is a common frame for constructing variational models for image processing,where the regularizer is the key to success.Regularizer corresponds to the a priori of MAP,which depicts the statistical properties of random variables.Although natural images involve different contents,their gradient histograms commonly follow Generalized Gaussian distribution(GGD),and this distribution provides us a good start point of our research.In one respect,when GGD is adopted for the a priori,the regularizer is equivalent to the Lp-norm,which is a natural non-convex extension of traditional convex norms,and in possession of stronger capabilities of sparsity inducing.Besides,as histogram is the statistical description of an image,histogram related constraint can supplement useful information for image processing.Based on these two considerations,we propose two regularization models,Lp-norm based model and histogram matching based model.For the research on cross-modality face synthesis,even though existing methods can achieve a good result of style transfer,they usually perform poorly at synthesizing facial details.To further enhance details,a two-step algorithm is proposed in this thesis.Compared with existing methods,there are three innovations in this part.First,facial images are processed separately for different areas.Second,by adopting the sparse structured matching method,the synthesis of facial components contains more details.Third,by constructing the LpLp-norm variational model,detail transfer from source modality to target modality is realized.For the research on image texture smoothing,edge-aware models are always the focus.Simply depending on the scale difference between image contour and textures cannot effectively lead to texture smoothing while preserving edges.In this thesis,based on the observation of smoothing images,we propose to divide an image into contour and non-contour areas.And two separate GGDs are constructed for each area,which are combined together with the help of structured random forests model to generate the Lpnorm mixture model.This model can better represent the properties of different areas,in contrast to traditional single norm based model.Ascribe to the discriminative capability of contour learning,the proposed mixture model can generate shaper edges.For the research on image denoising,natural image statistics is always the most important.Although sparse representation and nonlocal self-similarity based models achieve plausible results from the perspective of performance indexes,these models may oversmooth the areas with weak textures,and make these areas unnatural.In this thesis,we combine the histogram matching based regularization model with sparse representation based model to construct the variational.To further improve denoising in localized area,we propose two area division strategies.To estimate the reference histogram from noisy image,we propose the regularized deconvolutional algorithm.Experimental analysis proves that the prosed histogram estimation method can achieve high performance.In comparison with the state-of-the-art methods,histogram matching based model has advantages in image denoising.For the research on image deblurring,natural image statistics is also important.The weak textures turn even weaker due to the existence of blur kernel,and they are often taken as belonging to smooth areas and hard to retrieve.To improve the restoration in those areas,in this thesis,we propose a histogram matching based texture enhancement algorithm.This algorithm combines Lp-norm and histogram matching,and is solved using the method of half-quadratic variable splitting.To realize histogram estimation,we propose to adopt the Bayesian non-parametric regression model.Extensive experiments validate that our histogram estimation method is valid,and histogram matching can effectively enhance image details for image deblurring.